Textbook Problem

$33-40$ Intersection of Events These exercises involve the probability of the intersection of events.

A drawer contains an unorganized collection of $18$ socks. Three pairs are red, two pairs are white, and four pairs are black.

(a) If one sock is drawn at random from the drawer, what is the probability that it is red?

(b) Once a sock is drawn and discovered to be red, what is the probability of drawing another red sock next to make a matching pair?

(c) If two socks are drawn from the drawer at the same time, what is the probability that both are red?